Introduction to Acoustics

with equalization, without incurring unduly high-power
requirements.
In general, most musical and speech energy is concentrated
in a subset of the audio band, say from 100 Hz
to 10 kHz, allowing the majority of audio signals to be
satisfactorily reproduced with modestly compromised
system bandwidth, to the benefit of size, cost, and
bulk.
18.3.2 Amplitude Response Variation
From the basic amplitude acuity of the ear, it is logical
to require that the pass-band deviation in frequency
response be less than an amplitude JND, say within
± 0.25 dB of flat. Of course, this is the desired net response
of an entire signal chain, and if deviations are
known to exist in one part of the chain, it may be possible
to apply compensating equalization elsewhere in the
chain.
As with the quest for full audio bandwidth, early
audio systems for many years had trouble meeting this
requirement, in part from mechanical limitations. Amplifiers
again have traditionally had the easiest time
meeting this specification, and modern-day DSP is
limited only by the precision of the analog/digital
converters, which is generally quite good in this regard,
plus any deliberate signal-processing spectral
modifications.
The worst offender is many cases is the listening
room, where echoes and resonances are likely to
make nearly any sine-wave frequency response plot
a jumble of peaks and dips covering many dB. The threedimensionality
of the room and the fact that echoes arrive
from diverse directions work to reduce the audibility of
many of these measured deviations.
After rooms, loudspeakers have the hardest time
meeting this flat-response requirement, being mechanical
devices and having to handle a lot of power and
move a lot of air. In order to cover the bulk of the audio
band, loudspeaker designs typically employ multiple
drivers, each optimized for a portion of the audio band,
but this in turn introduces potential response deviations
from required crossover networks.
In considering reasonable values for most audio
specifications based on psychophysical performance, it
is prudent to consider both monotic and dichotic performance;
that is, each ear considered in isolation, and then
the binaural performance of the two ears together. In the
case of amplitude response variation, similar JNDs apply,
so there is no compelling reason to differentiate the
situations in this case.
Audio and Electroacoustics 18.3 Audio Specifications 753
18.3.3 Phase Response
In the course of passing through an audio component, an
audio signal may encounter delays, which may be frequency
dependent, and may therefore be categorized as
either frequency-dependent time delays, group delays,
or phase shifts. It is therefore prudent to establish preferred
perceptual limits on the allowable deviations of
these quantities.
Of course, a pure wide-band time delay will be manifested
as a linear change in phase shift proportional to
frequency, so to separate the effects of time delay and
phase shift, so the latter (“frequency-differential singlechannel
phase shift”) may commonly be understood
to represent the deviation from a linear-with-frequency
phase characteristic.
It is a little difficult to be completely definitive
about a phase-shift specification, in part because there
are multiple neural timing mechanisms involved. For
a sound channel considered in isolation, phase perception
is rather weak. There does not seem to be an explicit
means of comparing the fine-grain phase or timing of
signals at significantly different frequencies (more than
a critical bandwidth), at least for steady-state signals.
This is sometimes used as the basis of a claim that the
ear is virtually phase deaf, although that is probably
an overstatement. Still, if one constructs a steady-state
signal with widely space spectral components that are
in slow precession, say a combination of 100 Hz and
501 Hz (360 ◦ per second relative phase precession), the
resulting percept is almost entirely constant.
So under what conditions are phase shifts audible?
There seem to be at least three such mechanisms: fusion
time, transient fusion time, and critical band envelopes.
As noted earlier, fusion time refers to the audio event
integration time of the ear, generally in the range of
20–50 ms. Separate audio events that occur farther apart
than the fusion time will generally be heard as separate.
If a spectrally complex signal is put through a system
where some frequencies are phase- or time-shifted by
more than the fusion time, the signal may temporally
defuse, rendering the phase shift quite audible. (A 20 ms
phase delay at 30 Hz corresponds to 216 degrees of phase
shift, not an unrealistically large value.) This can occur,
for example, if a sharp pulse is passed through a thirdorder,
1/3-octave filter bank tuned for flat magnitude
response. What starts out as a click will emerge as a
“boing”, quite audibly distinct from the source.
Transient fusion time refers to the shortest interval
the ear can differentiate temporally, as exemplified by
the premasking interval of about 1–2 ms. If a sharp tran-
Part E 18.3